Extrapolation in quantum chemistry: Insights on energetics and reaction dynamics

Abstract

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-[Formula: see text]J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.

Canonical versus explicitly correlated coupled cluster: Post‐complete‐basis‐set extrapolation and the quest of the complete‐basis‐set limit

“…Yet, all systems in the present work were at (or nearby) the equilibrium geometry. Although the general expectation is that the approach should perform comfortably even far from equilibrium [59,73,74] (and references therein), a recent study [75] on the helium dimer alerts for difficulties in the short range region with the two‐point CBS scheme there employed. Of course, the ab initio theory itself may not generally perform uniformly over the entire configuration space.…”

“…Of course, the ab initio theory itself may not generally perform uniformly over the entire configuration space. Since nobody knows, and probably nobody has the tools yet to predict the best way to proceed, (physics‐based) extrapolation likewise interpolation (so much used in the spotlighted artificial intelligence) may offer a way toward cost‐effective quantum chemistry [27,74].…”

Reconciling spectroscopy with dynamics in global potential energy surfaces: The case of the astrophysically relevant SiC2

“…The MR set is in turn responsible to cover the bulk of the PES 43 , being restricted to sample the fragmentation region and geometries with high T 1 and D 1 diagnostics 44,45 [e.g., those characterized by larger C−C bond distances, away from the equilibrium region; see Figure 3(a) later]. Both data sets were subsequently extrapolated to the CBS limit 46,47 (see below). The AVXZ (X =T, Q, 5) basis sets of Dunning and co-workers 48,49 including additional tight-d functions (+d) for the Si atom 38 were employed throughout.…”

Optimized Structural Data at the Complete Basis Set Limit via Successive Quadratic Minimizations

“…In previous work, − we discussed how the complete basis set limit (CBS) of the correlation and SCF (HF and CASSCF) energies can be obtained via low-cost extrapolation methods; the reader is addressed elsewhere , for reviews. The extrapolation procedure is based on the re-hierarchization of the cardinal numbers used to define the basis set quality and has been shown to be applicable to any ansatz.…”